Table 2 Numeric results of \(w(y,t)\) for Example 2.

From: Analytical and numerical solutions of MABC fractional advection dispersion models by utilizing the modified physics informed neural networks with impacts of fractional derivative

\((y,t)\)

Approximate

Exact

Absolute Error

Error in  56

Error in  57

(0.2,0.2)

– 0.00001

– 0.00001

\(4.75 \times 10^{-16}\)

\(8.9101 \times 10^{-15}\)

\(3.0812 \times 10^{-3}\)

(0.4,0.4)

– 0.0004

– 0.0004

\(5.34 \times 10^{-15}\)

\(4.0724 \times 10^{-14}\)

\(2.5758 \times 10^{-3}\)

(0.6,0.6)

0.00074

0.00074

\(2.56 \times 10^{-14}\)

\(1.0467 \times 10^{-13}\)

\(8.1993 \times 10^{-3}\)

(0.8,0.8)

0.0034

0.0034

\(1.03 \times 10^{-13}\)

\(2.4097 \times 10^{-13}\)

\(1.7291 \times 10^{-3}\)